
where \(\mathbf {u}=[u_1,u_2]^T\)  is a concentration tensor, \(\mathbf {D}=\operatorname{diag}[D_1,D_2]^T\)  is a diffusion tensor and \( \mathbf {f} = [f_1(u_1,u_2), f_2(u_1,u_2)]^T\)  is a coupled reaction source term. First proposed by Turing [1]}, the reaction-diffusion equations are useful for understanding pattern formation and self-organization in biological and chemical systems [2]}, [3]}, such as morphogenesis [4]} and autocatalysis [5]}.
